That's a bit of a tough call. I haven't sailed the EVO IQ 76 but used the 2010 Quad 76 a lot and it's the same shape. Despite that the twin fin setup in the EVO IQ will surely soften the ride a bit, I think it's gonna be a bit too much board for the good days. Awesome for 5.3 and light 4.7 though.
The new EVO IQ 71 is a new shape. I have it but need some wind to get on water experience. But based on my experience with it's predecessors I'd say 5.3 is surely within reach and could even be very good. At your weight you can forget about the sail sizes on the web site. I'm also just above 70 and all EVOs, ETs, Quads in the Starboard lineup around this size always worked super well with 5.3 and even OK with bigger sails. We're still talking a 56cm wide shape. For more B&J style sailing when you want extra straight line effectiveness with the 5.3 you can also use a (slightly bigger) single fin. And in 4.7 stuff, even underpowered, you will definitley find the E71 very effective and I'm sure that from powered up 4.7 and windier, you will feel more comfy on the 71.
So, the more I wrote about it, the more clear it seems the 71 is the logical choice, right? I'm 100 % sure btw, that the E71 will feel more effective in underpowered 5.3 than your NewWave.